| Title:
|
Mapping theorems on countable tightness and a question of F. Siwiec (English) |
| Author:
|
Lin, Shou |
| Author:
|
Zhang, Jinhuang |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
55 |
| Issue:
|
4 |
| Year:
|
2014 |
| Pages:
|
523-536 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper $ss$-quotient maps and $ssq$-spaces are introduced. It is shown that (1) countable tightness is characterized by $ss$-quotient maps and quotient maps; (2) a space has countable tightness if and only if it is a countably bi-quotient image of a locally countable space, which gives an answer for a question posed by F. Siwiec in 1975; (3) $ssq$-spaces are characterized as the $ss$-quotient images of metric spaces; (4) assuming $2^\omega<2^{\omega_1}$, a compact $T_2$-space is an $ssq$-space if and only if every countably compact subset is strongly sequentially closed, which improves some results about sequential spaces obtained by M. Ismail and P. Nyikos in 1980. (English) |
| Keyword:
|
countable tightness |
| Keyword:
|
strongly sequentially closed sets |
| Keyword:
|
sequentially closed sets |
| Keyword:
|
quotient maps |
| Keyword:
|
countably bi-quotient maps |
| Keyword:
|
locally countable spaces |
| MSC:
|
54B15 |
| MSC:
|
54D55 |
| MSC:
|
54E40 |
| idZBL:
|
Zbl 06391560 |
| idMR:
|
MR3269014 |
| . |
| Date available:
|
2014-10-09T10:01:07Z |
| Last updated:
|
2017-01-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143976 |
| . |
| Reference:
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| Reference:
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